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<div class="header">
  <div class="summary">
<a href="classEigen_1_1FullPivLU-members.html">List of all members</a> &#124;
<a href="#pub-methods">Public Member Functions</a>  </div>
  <div class="headertitle">
<div class="title">Eigen::FullPivLU&lt; MatrixType_ &gt; Class Template Reference<div class="ingroups"><a class="el" href="group__DenseLinearSolvers__chapter.html">Dense linear problems and decompositions</a> &raquo; <a class="el" href="group__DenseLinearSolvers__Reference.html">Reference</a> &raquo; <a class="el" href="group__LU__Module.html">LU module</a></div></div>  </div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename MatrixType_&gt;<br />
class Eigen::FullPivLU&lt; MatrixType_ &gt;</h3>

<p>LU decomposition of a matrix with complete pivoting, and related features. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
  <table class="tparams">
    <tr><td class="paramname">MatrixType_</td><td>the type of the matrix of which we are computing the LU decomposition</td></tr>
  </table>
  </dd>
</dl>
<p>This class represents a LU decomposition of any matrix, with complete pivoting: the matrix A is decomposed as \( A = P^{-1} L U Q^{-1} \) where L is unit-lower-triangular, U is upper-triangular, and P and Q are permutation matrices. This is a rank-revealing LU decomposition. The eigenvalues (diagonal coefficients) of U are sorted in such a way that any zeros are at the end.</p>
<p>This decomposition provides the generic approach to solving systems of linear equations, computing the rank, invertibility, inverse, kernel, and determinant.</p>
<p>This LU decomposition is very stable and well tested with large matrices. However there are use cases where the SVD decomposition is inherently more stable and/or flexible. For example, when computing the kernel of a matrix, working with the SVD allows to select the smallest singular values of the matrix, something that the LU decomposition doesn't see.</p>
<p>The data of the LU decomposition can be directly accessed through the methods <a class="el" href="classEigen_1_1FullPivLU.html#a3e7d7a53f5b7c4ba99013fe171ac5654">matrixLU()</a>, <a class="el" href="classEigen_1_1FullPivLU.html#a3eb3aa0c37e06ffaf0c07b1eeb0995cc">permutationP()</a>, <a class="el" href="classEigen_1_1FullPivLU.html#a25b70ffbc88d804981c8874da55e7419">permutationQ()</a>.</p>
<p>As an example, here is how the original matrix can be retrieved: </p><div class="fragment"><div class="line"><span class="keyword">typedef</span> Matrix&lt;double, 5, 3&gt; Matrix5x3;</div>
<div class="line"><span class="keyword">typedef</span> Matrix&lt;double, 5, 5&gt; Matrix5x5;</div>
<div class="line">Matrix5x3 m = Matrix5x3::Random();</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is the matrix m:&quot;</span> &lt;&lt; endl &lt;&lt; m &lt;&lt; endl;</div>
<div class="line"><a class="code" href="classEigen_1_1FullPivLU.html">Eigen::FullPivLU&lt;Matrix5x3&gt;</a> lu(m);</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is, up to permutations, its LU decomposition matrix:&quot;</span></div>
<div class="line">     &lt;&lt; endl &lt;&lt; lu.matrixLU() &lt;&lt; endl;</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is the L part:&quot;</span> &lt;&lt; endl;</div>
<div class="line">Matrix5x5 l = Matrix5x5::Identity();</div>
<div class="line">l.block&lt;5,3&gt;(0,0).triangularView&lt;StrictlyLower&gt;() = lu.matrixLU();</div>
<div class="line">cout &lt;&lt; l &lt;&lt; endl;</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is the U part:&quot;</span> &lt;&lt; endl;</div>
<div class="line">Matrix5x3 u = lu.matrixLU().triangularView&lt;<a class="code" href="group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdafca2ccebb604f171656deb53e8c083c1">Upper</a>&gt;();</div>
<div class="line">cout &lt;&lt; u &lt;&lt; endl;</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Let us now reconstruct the original matrix m:&quot;</span> &lt;&lt; endl;</div>
<div class="line">cout &lt;&lt; lu.permutationP().inverse() * l * u * lu.permutationQ().inverse() &lt;&lt; endl;</div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html"><div class="ttname"><a href="classEigen_1_1FullPivLU.html">Eigen::FullPivLU</a></div><div class="ttdoc">LU decomposition of a matrix with complete pivoting, and related features.</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:64</div></div>
<div class="ttc" id="agroup__enums_html_gga39e3366ff5554d731e7dc8bb642f83cdafca2ccebb604f171656deb53e8c083c1"><div class="ttname"><a href="group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdafca2ccebb604f171656deb53e8c083c1">Eigen::Upper</a></div><div class="ttdeci">@ Upper</div><div class="ttdef"><b>Definition:</b> Constants.h:213</div></div>
</div><!-- fragment --><p> Output: </p><pre class="fragment">Here is the matrix m:
   0.68  -0.605 -0.0452
 -0.211   -0.33   0.258
  0.566   0.536   -0.27
  0.597  -0.444  0.0268
  0.823   0.108   0.904
Here is, up to permutations, its LU decomposition matrix:
 0.904  0.823  0.108
-0.299  0.812  0.569
 -0.05  0.888   -1.1
0.0296  0.705  0.768
 0.285 -0.549 0.0436
Here is the L part:
     1      0      0      0      0
-0.299      1      0      0      0
 -0.05  0.888      1      0      0
0.0296  0.705  0.768      1      0
 0.285 -0.549 0.0436      0      1
Here is the U part:
0.904 0.823 0.108
    0 0.812 0.569
    0     0  -1.1
    0     0     0
    0     0     0
Let us now reconstruct the original matrix m:
   0.68  -0.605 -0.0452
 -0.211   -0.33   0.258
  0.566   0.536   -0.27
  0.597  -0.444  0.0268
  0.823   0.108   0.904
</pre><p>This class supports the <a class="el" href="group__InplaceDecomposition.html">inplace decomposition </a> mechanism.</p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#a25da97d31acab0ee5d9d13bdbb0569da">MatrixBase::fullPivLu()</a>, <a class="el" href="classEigen_1_1MatrixBase.html#a7ad8f77004bb956b603bb43fd2e3c061">MatrixBase::determinant()</a>, <a class="el" href="classEigen_1_1MatrixBase.html#a7712eb69e8ea3c8f7b8da1c44dbdeebf">MatrixBase::inverse()</a> </dd></dl>
</div><div id="dynsection-0" onclick="return toggleVisibility(this)" class="dynheader closed" style="cursor:pointer;">
  <img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for Eigen::FullPivLU&lt; MatrixType_ &gt;:</div>
<div id="dynsection-0-summary" class="dynsummary" style="display:block;">
</div>
<div id="dynsection-0-content" class="dyncontent" style="display:none;">
<div class="center"><img src="classEigen_1_1FullPivLU__inherit__graph.png" border="0" usemap="#aEigen_1_1FullPivLU_3_01MatrixType___01_4_inherit__map" alt="Inheritance graph"/></div>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a396f63d737e0613f41004e30be8fe3cf"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:a396f63d737e0613f41004e30be8fe3cf"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1FullPivLU.html">FullPivLU</a> &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#a396f63d737e0613f41004e30be8fe3cf">compute</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix)</td></tr>
<tr class="separator:a396f63d737e0613f41004e30be8fe3cf"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a71654e5c60a26407ecccfaa5b34bb0aa"><td class="memItemLeft" align="right" valign="top">internal::traits&lt; MatrixType &gt;::Scalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#a71654e5c60a26407ecccfaa5b34bb0aa">determinant</a> () const</td></tr>
<tr class="separator:a71654e5c60a26407ecccfaa5b34bb0aa"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a358cec49914ec3cd3707e6b79ae32d0b"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#a358cec49914ec3cd3707e6b79ae32d0b">dimensionOfKernel</a> () const</td></tr>
<tr class="separator:a358cec49914ec3cd3707e6b79ae32d0b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af225528d1c6e623a2b1dce091907d13e"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#af225528d1c6e623a2b1dce091907d13e">FullPivLU</a> ()</td></tr>
<tr class="memdesc:af225528d1c6e623a2b1dce091907d13e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default Constructor.  <a href="classEigen_1_1FullPivLU.html#af225528d1c6e623a2b1dce091907d13e">More...</a><br /></td></tr>
<tr class="separator:af225528d1c6e623a2b1dce091907d13e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a31a6a984478a9f721f367667fe4c5ab1"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:a31a6a984478a9f721f367667fe4c5ab1"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#a31a6a984478a9f721f367667fe4c5ab1">FullPivLU</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix)</td></tr>
<tr class="separator:a31a6a984478a9f721f367667fe4c5ab1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3e903b9f401e3fc5d1ca7c6951c76185"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:a3e903b9f401e3fc5d1ca7c6951c76185"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#a3e903b9f401e3fc5d1ca7c6951c76185">FullPivLU</a> (<a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix)</td></tr>
<tr class="memdesc:a3e903b9f401e3fc5d1ca7c6951c76185"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructs a LU factorization from a given matrix.  <a href="classEigen_1_1FullPivLU.html#a3e903b9f401e3fc5d1ca7c6951c76185">More...</a><br /></td></tr>
<tr class="separator:a3e903b9f401e3fc5d1ca7c6951c76185"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae83ebd2a24088f04e3ac835b0dc001e1"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#ae83ebd2a24088f04e3ac835b0dc001e1">FullPivLU</a> (<a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> rows, <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols)</td></tr>
<tr class="memdesc:ae83ebd2a24088f04e3ac835b0dc001e1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default Constructor with memory preallocation.  <a href="classEigen_1_1FullPivLU.html#ae83ebd2a24088f04e3ac835b0dc001e1">More...</a><br /></td></tr>
<tr class="separator:ae83ebd2a24088f04e3ac835b0dc001e1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa8cbf984141608e89b503125690d24d4"><td class="memItemLeft" align="right" valign="top">const internal::image_retval&lt; <a class="el" href="classEigen_1_1FullPivLU.html">FullPivLU</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#aa8cbf984141608e89b503125690d24d4">image</a> (const MatrixType &amp;originalMatrix) const</td></tr>
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<tr class="memitem:a34afc848d7fb22c7a56a053d3807d2cd"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Inverse.html">Inverse</a>&lt; <a class="el" href="classEigen_1_1FullPivLU.html">FullPivLU</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#a34afc848d7fb22c7a56a053d3807d2cd">inverse</a> () const</td></tr>
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<tr class="memitem:a90dd33c632ba890175f61eac054bde98"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#a90dd33c632ba890175f61eac054bde98">isInjective</a> () const</td></tr>
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<tr class="memitem:a0ee7753645eb31bcbd5faa459168b294"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#a0ee7753645eb31bcbd5faa459168b294">isInvertible</a> () const</td></tr>
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<tr class="memitem:af42b9cb6356658b92b2d1006aee73fc4"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#af42b9cb6356658b92b2d1006aee73fc4">isSurjective</a> () const</td></tr>
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<tr class="memitem:adfc1e27ff60287be5313b5efc3559308"><td class="memItemLeft" align="right" valign="top">const internal::kernel_retval&lt; <a class="el" href="classEigen_1_1FullPivLU.html">FullPivLU</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#adfc1e27ff60287be5313b5efc3559308">kernel</a> () const</td></tr>
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<tr class="memitem:a3e7d7a53f5b7c4ba99013fe171ac5654"><td class="memItemLeft" align="right" valign="top">const MatrixType &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#a3e7d7a53f5b7c4ba99013fe171ac5654">matrixLU</a> () const</td></tr>
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<tr class="memitem:a05cedf8dca6394355ef64c1ea1374b4a"><td class="memItemLeft" align="right" valign="top">RealScalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#a05cedf8dca6394355ef64c1ea1374b4a">maxPivot</a> () const</td></tr>
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<tr class="memitem:aad90c46ea08618ae485fce4e5f4677d0"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#aad90c46ea08618ae485fce4e5f4677d0">nonzeroPivots</a> () const</td></tr>
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<tr class="memitem:a3eb3aa0c37e06ffaf0c07b1eeb0995cc"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1PermutationMatrix.html">PermutationPType</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#a3eb3aa0c37e06ffaf0c07b1eeb0995cc">permutationP</a> () const</td></tr>
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<tr class="memitem:a25b70ffbc88d804981c8874da55e7419"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1PermutationMatrix.html">PermutationQType</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#a25b70ffbc88d804981c8874da55e7419">permutationQ</a> () const</td></tr>
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<tr class="memitem:a8d31c78a17a70d56ef2d105d6b5efec3"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#a8d31c78a17a70d56ef2d105d6b5efec3">rank</a> () const</td></tr>
<tr class="separator:a8d31c78a17a70d56ef2d105d6b5efec3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae39fcfa8d1319472a5b2adfa7a28d9cf"><td class="memItemLeft" align="right" valign="top">RealScalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#ae39fcfa8d1319472a5b2adfa7a28d9cf">rcond</a> () const</td></tr>
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<tr class="memitem:a191a4f598b0c192a83ab48984e87ee51"><td class="memItemLeft" align="right" valign="top">MatrixType&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#a191a4f598b0c192a83ab48984e87ee51">reconstructedMatrix</a> () const</td></tr>
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<tr class="memitem:abad257b6db0856d8ec52c6072f58f75d"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1FullPivLU.html">FullPivLU</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#abad257b6db0856d8ec52c6072f58f75d">setThreshold</a> (const RealScalar &amp;<a class="el" href="classEigen_1_1FullPivLU.html#ae2298a7a89749dee7d86f02ccacce0cb">threshold</a>)</td></tr>
<tr class="separator:abad257b6db0856d8ec52c6072f58f75d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aeafbb0b885cc4c28b53e77988ac5cfe3"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1FullPivLU.html">FullPivLU</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#aeafbb0b885cc4c28b53e77988ac5cfe3">setThreshold</a> (Default_t)</td></tr>
<tr class="separator:aeafbb0b885cc4c28b53e77988ac5cfe3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a614d3aa28e6af7b2af8630d3e2d022d8"><td class="memTemplParams" colspan="2">template&lt;typename Rhs &gt; </td></tr>
<tr class="memitem:a614d3aa28e6af7b2af8630d3e2d022d8"><td class="memTemplItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Solve.html">Solve</a>&lt; <a class="el" href="classEigen_1_1FullPivLU.html">FullPivLU</a>, Rhs &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#a614d3aa28e6af7b2af8630d3e2d022d8">solve</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Rhs &gt; &amp;b) const</td></tr>
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<tr class="memitem:ae2298a7a89749dee7d86f02ccacce0cb"><td class="memItemLeft" align="right" valign="top">RealScalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1FullPivLU.html#ae2298a7a89749dee7d86f02ccacce0cb">threshold</a> () const</td></tr>
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<tr class="inherit_header pub_methods_classEigen_1_1SolverBase"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_classEigen_1_1SolverBase')"><img src="closed.png" alt="-"/>&#160;Public Member Functions inherited from <a class="el" href="classEigen_1_1SolverBase.html">Eigen::SolverBase&lt; FullPivLU&lt; MatrixType_ &gt; &gt;</a></td></tr>
<tr class="memitem:ae1025416bdb5a768f7213c67feb4dc33 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const AdjointReturnType&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#ae1025416bdb5a768f7213c67feb4dc33">adjoint</a> () const</td></tr>
<tr class="separator:ae1025416bdb5a768f7213c67feb4dc33 inherit pub_methods_classEigen_1_1SolverBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1FullPivLU.html">FullPivLU</a>&lt; MatrixType_ &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a> ()</td></tr>
<tr class="separator:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_classEigen_1_1SolverBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1FullPivLU.html">FullPivLU</a>&lt; MatrixType_ &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#afd4f3f1c57b7594b96a7e30f2974ea2e">derived</a> () const</td></tr>
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<tr class="memitem:a7fd647d110487799205df6f99547879d inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Solve.html">Solve</a>&lt; <a class="el" href="classEigen_1_1FullPivLU.html">FullPivLU</a>&lt; MatrixType_ &gt;, Rhs &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a7fd647d110487799205df6f99547879d">solve</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Rhs &gt; &amp;b) const</td></tr>
<tr class="separator:a7fd647d110487799205df6f99547879d inherit pub_methods_classEigen_1_1SolverBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4d5e5baddfba3790ab1a5f247dcc4dc1 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a4d5e5baddfba3790ab1a5f247dcc4dc1">SolverBase</a> ()</td></tr>
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<tr class="memitem:a70cf5cd1b31dbb4f4d61c436c83df6d3 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Transpose.html">ConstTransposeReturnType</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a70cf5cd1b31dbb4f4d61c436c83df6d3">transpose</a> () const</td></tr>
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<tr class="inherit_header pub_methods_structEigen_1_1EigenBase"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_structEigen_1_1EigenBase')"><img src="closed.png" alt="-"/>&#160;Public Member Functions inherited from <a class="el" href="structEigen_1_1EigenBase.html">Eigen::EigenBase&lt; Derived &gt;</a></td></tr>
<tr class="memitem:a2d768a9877f5f69f49432d447b552bfe inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a2d768a9877f5f69f49432d447b552bfe">cols</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="memitem:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">Derived &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a> ()</td></tr>
<tr class="separator:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_structEigen_1_1EigenBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">const Derived &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#afd4f3f1c57b7594b96a7e30f2974ea2e">derived</a> () const</td></tr>
<tr class="separator:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_structEigen_1_1EigenBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ac22eb0695d00edd7d4a3b2d0a98b81c2 inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="memitem:ae106171b6fefd3f7af108a8283de36c9 inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a> () const EIGEN_NOEXCEPT</td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="inherited"></a>
Additional Inherited Members</h2></td></tr>
<tr class="inherit_header pub_types_structEigen_1_1EigenBase"><td colspan="2" onclick="javascript:toggleInherit('pub_types_structEigen_1_1EigenBase')"><img src="closed.png" alt="-"/>&#160;Public Types inherited from <a class="el" href="structEigen_1_1EigenBase.html">Eigen::EigenBase&lt; Derived &gt;</a></td></tr>
<tr class="memitem:a554f30542cc2316add4b1ea0a492ff02 inherit pub_types_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a></td></tr>
<tr class="memdesc:a554f30542cc2316add4b1ea0a492ff02 inherit pub_types_structEigen_1_1EigenBase"><td class="mdescLeft">&#160;</td><td class="mdescRight">The interface type of indices.  <a href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">More...</a><br /></td></tr>
<tr class="separator:a554f30542cc2316add4b1ea0a492ff02 inherit pub_types_structEigen_1_1EigenBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="af225528d1c6e623a2b1dce091907d13e"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af225528d1c6e623a2b1dce091907d13e">&#9670;&nbsp;</a></span>FullPivLU() <span class="overload">[1/4]</span></h2>

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template&lt;typename MatrixType &gt; </div>
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<p>Default Constructor. </p>
<p>The default constructor is useful in cases in which the user intends to perform decompositions via LU::compute(const MatrixType&amp;). </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ae83ebd2a24088f04e3ac835b0dc001e1">&#9670;&nbsp;</a></span>FullPivLU() <span class="overload">[2/4]</span></h2>

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template&lt;typename MatrixType &gt; </div>
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          <td class="memname"><a class="el" href="classEigen_1_1FullPivLU.html">Eigen::FullPivLU</a>&lt; MatrixType &gt;::<a class="el" href="classEigen_1_1FullPivLU.html">FullPivLU</a> </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td>
          <td class="paramname"><em>rows</em>, </td>
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          <td></td>
          <td class="paramtype"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td>
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          <td>)</td>
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<p>Default Constructor with memory preallocation. </p>
<p>Like the default constructor but with preallocation of the internal data according to the specified problem <em>size</em>. </p><dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1FullPivLU.html#af225528d1c6e623a2b1dce091907d13e" title="Default Constructor.">FullPivLU()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a31a6a984478a9f721f367667fe4c5ab1">&#9670;&nbsp;</a></span>FullPivLU() <span class="overload">[3/4]</span></h2>

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template&lt;typename MatrixType &gt; </div>
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          <td class="memname"><a class="el" href="classEigen_1_1FullPivLU.html">Eigen::FullPivLU</a>&lt; MatrixType &gt;::<a class="el" href="classEigen_1_1FullPivLU.html">FullPivLU</a> </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;&#160;</td>
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<p>Constructor.</p>
<dl class="params"><dt>Parameters</dt><dd>
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    <tr><td class="paramname">matrix</td><td>the matrix of which to compute the LU decomposition. It is required to be nonzero. </td></tr>
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<h2 class="memtitle"><span class="permalink"><a href="#a3e903b9f401e3fc5d1ca7c6951c76185">&#9670;&nbsp;</a></span>FullPivLU() <span class="overload">[4/4]</span></h2>

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template&lt;typename MatrixType &gt; </div>
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          <td>(</td>
          <td class="paramtype"><a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;&#160;</td>
          <td class="paramname"><em>matrix</em></td><td>)</td>
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<p>Constructs a LU factorization from a given matrix. </p>
<p>This overloaded constructor is provided for <a class="el" href="group__InplaceDecomposition.html">inplace decomposition </a> when <code>MatrixType</code> is a <a class="el" href="classEigen_1_1Ref.html" title="A matrix or vector expression mapping an existing expression.">Eigen::Ref</a>.</p>
<dl class="section see"><dt>See also</dt><dd>FullPivLU(const EigenBase&amp;) </dd></dl>

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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a396f63d737e0613f41004e30be8fe3cf">&#9670;&nbsp;</a></span>compute()</h2>

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template&lt;typename MatrixType_ &gt; </div>
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template&lt;typename InputType &gt; </div>
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          <td class="memname"><a class="el" href="classEigen_1_1FullPivLU.html">FullPivLU</a>&amp; <a class="el" href="classEigen_1_1FullPivLU.html">Eigen::FullPivLU</a>&lt; MatrixType_ &gt;::compute </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;&#160;</td>
          <td class="paramname"><em>matrix</em></td><td>)</td>
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<p>Computes the LU decomposition of the given matrix.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">matrix</td><td>the matrix of which to compute the LU decomposition. It is required to be nonzero.</td></tr>
  </table>
  </dd>
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<dl class="section return"><dt>Returns</dt><dd>a reference to *this </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a71654e5c60a26407ecccfaa5b34bb0aa">&#9670;&nbsp;</a></span>determinant()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the determinant of the matrix of which *this is the LU decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the LU decomposition has already been computed.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This is only for square matrices.</dd>
<dd>
For fixed-size matrices of size up to 4, <a class="el" href="classEigen_1_1MatrixBase.html#a7ad8f77004bb956b603bb43fd2e3c061">MatrixBase::determinant()</a> offers optimized paths.</dd></dl>
<dl class="section warning"><dt>Warning</dt><dd>a determinant can be very big or small, so for matrices of large enough dimension, there is a risk of overflow/underflow.</dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#a7ad8f77004bb956b603bb43fd2e3c061">MatrixBase::determinant()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a358cec49914ec3cd3707e6b79ae32d0b">&#9670;&nbsp;</a></span>dimensionOfKernel()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the dimension of the kernel of the matrix of which *this is the LU decomposition.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1FullPivLU.html#abad257b6db0856d8ec52c6072f58f75d">setThreshold(const RealScalar&amp;)</a>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#aa8cbf984141608e89b503125690d24d4">&#9670;&nbsp;</a></span>image()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the image of the matrix, also called its column-space. The columns of the returned matrix will form a basis of the image (column-space).</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
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<dl class="section note"><dt>Note</dt><dd>If the image has dimension zero, then the returned matrix is a column-vector filled with zeros.</dd>
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This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1FullPivLU.html#abad257b6db0856d8ec52c6072f58f75d">setThreshold(const RealScalar&amp;)</a>.</dd></dl>
<p>Example: </p><div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#ga84e9fd068879d808012bb6d5dbfecb17">Matrix3d</a> m;</div>
<div class="line">m &lt;&lt; 1,1,0,</div>
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<div class="line">     0,1,1;</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is the matrix m:&quot;</span> &lt;&lt; endl &lt;&lt; m &lt;&lt; endl;</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Notice that the middle column is the sum of the two others, so the &quot;</span></div>
<div class="line">     &lt;&lt; <span class="stringliteral">&quot;columns are linearly dependent.&quot;</span> &lt;&lt; endl;</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is a matrix whose columns have the same span but are linearly independent:&quot;</span></div>
<div class="line">     &lt;&lt; endl &lt;&lt; m.fullPivLu().image(m) &lt;&lt; endl;</div>
<div class="ttc" id="agroup__matrixtypedefs_html_ga84e9fd068879d808012bb6d5dbfecb17"><div class="ttname"><a href="group__matrixtypedefs.html#ga84e9fd068879d808012bb6d5dbfecb17">Eigen::Matrix3d</a></div><div class="ttdeci">Matrix&lt; double, 3, 3 &gt; Matrix3d</div><div class="ttdoc">3×3 matrix of type double.</div><div class="ttdef"><b>Definition:</b> Matrix.h:501</div></div>
</div><!-- fragment --><p> Output: </p><pre class="fragment">Here is the matrix m:
1 1 0
1 3 2
0 1 1
Notice that the middle column is the sum of the two others, so the columns are linearly dependent.
Here is a matrix whose columns have the same span but are linearly independent:
1 1
3 1
1 0
</pre><dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1FullPivLU.html#adfc1e27ff60287be5313b5efc3559308">kernel()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a34afc848d7fb22c7a56a053d3807d2cd">&#9670;&nbsp;</a></span>inverse()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the inverse of the matrix of which *this is the LU decomposition.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>If this matrix is not invertible, the returned matrix has undefined coefficients. Use <a class="el" href="classEigen_1_1FullPivLU.html#a0ee7753645eb31bcbd5faa459168b294">isInvertible()</a> to first determine whether this matrix is invertible.</dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#a7712eb69e8ea3c8f7b8da1c44dbdeebf">MatrixBase::inverse()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a90dd33c632ba890175f61eac054bde98">&#9670;&nbsp;</a></span>isInjective()</h2>

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<dl class="section return"><dt>Returns</dt><dd>true if the matrix of which *this is the LU decomposition represents an injective linear map, i.e. has trivial kernel; false otherwise.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1FullPivLU.html#abad257b6db0856d8ec52c6072f58f75d">setThreshold(const RealScalar&amp;)</a>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a0ee7753645eb31bcbd5faa459168b294">&#9670;&nbsp;</a></span>isInvertible()</h2>

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<dl class="section return"><dt>Returns</dt><dd>true if the matrix of which *this is the LU decomposition is invertible.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1FullPivLU.html#abad257b6db0856d8ec52c6072f58f75d">setThreshold(const RealScalar&amp;)</a>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#af42b9cb6356658b92b2d1006aee73fc4">&#9670;&nbsp;</a></span>isSurjective()</h2>

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<dl class="section return"><dt>Returns</dt><dd>true if the matrix of which *this is the LU decomposition represents a surjective linear map; false otherwise.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1FullPivLU.html#abad257b6db0856d8ec52c6072f58f75d">setThreshold(const RealScalar&amp;)</a>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#adfc1e27ff60287be5313b5efc3559308">&#9670;&nbsp;</a></span>kernel()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the kernel of the matrix, also called its null-space. The columns of the returned matrix will form a basis of the kernel.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>If the kernel has dimension zero, then the returned matrix is a column-vector filled with zeros.</dd>
<dd>
This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1FullPivLU.html#abad257b6db0856d8ec52c6072f58f75d">setThreshold(const RealScalar&amp;)</a>.</dd></dl>
<p>Example: </p><div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#ga731599f782380312960376c43450eb48">MatrixXf</a> m = <a class="code" href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">MatrixXf::Random</a>(3,5);</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is the matrix m:&quot;</span> &lt;&lt; endl &lt;&lt; m &lt;&lt; endl;</div>
<div class="line"><a class="code" href="group__matrixtypedefs.html#ga731599f782380312960376c43450eb48">MatrixXf</a> ker = m.fullPivLu().kernel();</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is a matrix whose columns form a basis of the kernel of m:&quot;</span></div>
<div class="line">     &lt;&lt; endl &lt;&lt; ker &lt;&lt; endl;</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;By definition of the kernel, m*ker is zero:&quot;</span></div>
<div class="line">     &lt;&lt; endl &lt;&lt; m*ker &lt;&lt; endl;</div>
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<div class="ttc" id="agroup__matrixtypedefs_html_ga731599f782380312960376c43450eb48"><div class="ttname"><a href="group__matrixtypedefs.html#ga731599f782380312960376c43450eb48">Eigen::MatrixXf</a></div><div class="ttdeci">Matrix&lt; float, Dynamic, Dynamic &gt; MatrixXf</div><div class="ttdoc">Dynamic×Dynamic matrix of type float.</div><div class="ttdef"><b>Definition:</b> Matrix.h:500</div></div>
</div><!-- fragment --><p> Output: </p><pre class="fragment">Here is the matrix m:
   0.68   0.597   -0.33   0.108   -0.27
 -0.211   0.823   0.536 -0.0452  0.0268
  0.566  -0.605  -0.444   0.258   0.904
Here is a matrix whose columns form a basis of the kernel of m:
 -0.219   0.763
0.00335  -0.447
      0       1
      1       0
 -0.145  -0.285
By definition of the kernel, m*ker is zero:
 7.45e-09  1.49e-08
-1.86e-09 -4.05e-08
        0 -2.98e-08
</pre><dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1FullPivLU.html#aa8cbf984141608e89b503125690d24d4">image()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a3e7d7a53f5b7c4ba99013fe171ac5654">&#9670;&nbsp;</a></span>matrixLU()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the LU decomposition matrix: the upper-triangular part is U, the unit-lower-triangular part is L (at least for square matrices; in the non-square case, special care is needed, see the documentation of class <a class="el" href="classEigen_1_1FullPivLU.html" title="LU decomposition of a matrix with complete pivoting, and related features.">FullPivLU</a>).</dd></dl>
<dl class="section see"><dt>See also</dt><dd>matrixL(), matrixU() </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a05cedf8dca6394355ef64c1ea1374b4a">&#9670;&nbsp;</a></span>maxPivot()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the absolute value of the biggest pivot, i.e. the biggest diagonal coefficient of U. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#aad90c46ea08618ae485fce4e5f4677d0">&#9670;&nbsp;</a></span>nonzeroPivots()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the number of nonzero pivots in the LU decomposition. Here nonzero is meant in the exact sense, not in a fuzzy sense. So that notion isn't really intrinsically interesting, but it is still useful when implementing algorithms.</dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1FullPivLU.html#a8d31c78a17a70d56ef2d105d6b5efec3">rank()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a3eb3aa0c37e06ffaf0c07b1eeb0995cc">&#9670;&nbsp;</a></span>permutationP()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the permutation matrix P</dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1FullPivLU.html#a25b70ffbc88d804981c8874da55e7419">permutationQ()</a> </dd></dl>

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<dl class="section return"><dt>Returns</dt><dd>the permutation matrix Q</dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1FullPivLU.html#a3eb3aa0c37e06ffaf0c07b1eeb0995cc">permutationP()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a8d31c78a17a70d56ef2d105d6b5efec3">&#9670;&nbsp;</a></span>rank()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the rank of the matrix of which *this is the LU decomposition.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1FullPivLU.html#abad257b6db0856d8ec52c6072f58f75d">setThreshold(const RealScalar&amp;)</a>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ae39fcfa8d1319472a5b2adfa7a28d9cf">&#9670;&nbsp;</a></span>rcond()</h2>

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<dl class="section return"><dt>Returns</dt><dd>an estimate of the reciprocal condition number of the matrix of which <code>*this</code> is the LU decomposition. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a191a4f598b0c192a83ab48984e87ee51">&#9670;&nbsp;</a></span>reconstructedMatrix()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the matrix represented by the decomposition, i.e., it returns the product: \( P^{-1} L U Q^{-1} \). This function is provided for debug purposes. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#abad257b6db0856d8ec52c6072f58f75d">&#9670;&nbsp;</a></span>setThreshold() <span class="overload">[1/2]</span></h2>

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          <td class="memname"><a class="el" href="classEigen_1_1FullPivLU.html">FullPivLU</a>&amp; <a class="el" href="classEigen_1_1FullPivLU.html">Eigen::FullPivLU</a>&lt; MatrixType_ &gt;::setThreshold </td>
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<p>Allows to prescribe a threshold to be used by certain methods, such as <a class="el" href="classEigen_1_1FullPivLU.html#a8d31c78a17a70d56ef2d105d6b5efec3">rank()</a>, who need to determine when pivots are to be considered nonzero. This is not used for the LU decomposition itself.</p>
<p>When it needs to get the threshold value, <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> calls <a class="el" href="classEigen_1_1FullPivLU.html#ae2298a7a89749dee7d86f02ccacce0cb">threshold()</a>. By default, this uses a formula to automatically determine a reasonable threshold. Once you have called the present method <a class="el" href="classEigen_1_1FullPivLU.html#abad257b6db0856d8ec52c6072f58f75d">setThreshold(const RealScalar&amp;)</a>, your value is used instead.</p>
<dl class="params"><dt>Parameters</dt><dd>
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<p>A pivot will be considered nonzero if its absolute value is strictly greater than \( \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert \) where maxpivot is the biggest pivot.</p>
<p>If you want to come back to the default behavior, call <a class="el" href="classEigen_1_1FullPivLU.html#aeafbb0b885cc4c28b53e77988ac5cfe3">setThreshold(Default_t)</a> </p>

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<h2 class="memtitle"><span class="permalink"><a href="#aeafbb0b885cc4c28b53e77988ac5cfe3">&#9670;&nbsp;</a></span>setThreshold() <span class="overload">[2/2]</span></h2>

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<p>Allows to come back to the default behavior, letting <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> use its default formula for determining the threshold.</p>
<p>You should pass the special object Eigen::Default as parameter here. </p><div class="fragment"><div class="line">lu.setThreshold(Eigen::Default); </div>
</div><!-- fragment --><p>See the documentation of <a class="el" href="classEigen_1_1FullPivLU.html#abad257b6db0856d8ec52c6072f58f75d">setThreshold(const RealScalar&amp;)</a>. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a614d3aa28e6af7b2af8630d3e2d022d8">&#9670;&nbsp;</a></span>solve()</h2>

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<dl class="section return"><dt>Returns</dt><dd>a solution x to the equation Ax=b, where A is the matrix of which *this is the LU decomposition.</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
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    <tr><td class="paramname">b</td><td>the right-hand-side of the equation to solve. Can be a vector or a matrix, the only requirement in order for the equation to make sense is that b.rows()==A.rows(), where A is the matrix of which *this is the LU decomposition.</td></tr>
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<dl class="section return"><dt>Returns</dt><dd>a solution.</dd></dl>
<p>This method just tries to find as good a solution as possible. If you want to check whether a solution exists or if it is accurate, just call this function to get a result and then compute the error of this result, or use <a class="el" href="classEigen_1_1DenseBase.html#ae8443357b808cd393be1b51974213f9c">MatrixBase::isApprox()</a> directly, for instance like this:</p><div class="fragment"><div class="line"><span class="keywordtype">bool</span> a_solution_exists = (A*result).isApprox(b, precision); </div>
</div><!-- fragment --><p> This method avoids dividing by zero, so that the non-existence of a solution doesn't by itself mean that you'll get <code>inf</code> or <code>nan</code> values.</p>
<p>If there exists more than one solution, this method will arbitrarily choose one. If you need a complete analysis of the space of solutions, take the one solution obtained by this method and add to it elements of the kernel, as determined by <a class="el" href="classEigen_1_1FullPivLU.html#adfc1e27ff60287be5313b5efc3559308">kernel()</a>.</p>
<p>Example: </p><div class="fragment"><div class="line">Matrix&lt;float,2,3&gt; m = <a class="code" href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">Matrix&lt;float,2,3&gt;::Random</a>();</div>
<div class="line"><a class="code" href="group__matrixtypedefs.html#ga36b8989b6aa63020139fc36bae6979e0">Matrix2f</a> y = <a class="code" href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">Matrix2f::Random</a>();</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is the matrix m:&quot;</span> &lt;&lt; endl &lt;&lt; m &lt;&lt; endl;</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is the matrix y:&quot;</span> &lt;&lt; endl &lt;&lt; y &lt;&lt; endl;</div>
<div class="line">Matrix&lt;float,3,2&gt; x = m.fullPivLu().solve(y);</div>
<div class="line"><span class="keywordflow">if</span>((m*x).isApprox(y))</div>
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<div class="line">  cout &lt;&lt; <span class="stringliteral">&quot;The equation mx=y does not have any solution.&quot;</span> &lt;&lt; endl;</div>
<div class="ttc" id="agroup__matrixtypedefs_html_ga36b8989b6aa63020139fc36bae6979e0"><div class="ttname"><a href="group__matrixtypedefs.html#ga36b8989b6aa63020139fc36bae6979e0">Eigen::Matrix2f</a></div><div class="ttdeci">Matrix&lt; float, 2, 2 &gt; Matrix2f</div><div class="ttdoc">2×2 matrix of type float.</div><div class="ttdef"><b>Definition:</b> Matrix.h:500</div></div>
</div><!-- fragment --><p> Output: </p><pre class="fragment">Here is the matrix m:
  0.68  0.566  0.823
-0.211  0.597 -0.605
Here is the matrix y:
 -0.33 -0.444
 0.536  0.108
Here is a solution x to the equation mx=y:
     0      0
 0.291 -0.216
  -0.6 -0.391
</pre><dl class="section see"><dt>See also</dt><dd>TriangularView::solve(), <a class="el" href="classEigen_1_1FullPivLU.html#adfc1e27ff60287be5313b5efc3559308">kernel()</a>, <a class="el" href="classEigen_1_1FullPivLU.html#a34afc848d7fb22c7a56a053d3807d2cd">inverse()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ae2298a7a89749dee7d86f02ccacce0cb">&#9670;&nbsp;</a></span>threshold()</h2>

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<p>Returns the threshold that will be used by certain methods such as <a class="el" href="classEigen_1_1FullPivLU.html#a8d31c78a17a70d56ef2d105d6b5efec3">rank()</a>.</p>
<p>See the documentation of <a class="el" href="classEigen_1_1FullPivLU.html#abad257b6db0856d8ec52c6072f58f75d">setThreshold(const RealScalar&amp;)</a>. </p>

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<hr/>The documentation for this class was generated from the following file:<ul>
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